In three experiments with a total number of 240 participants, the conditional event interpretation is the dominating interpretation of if–then sentences. About 75% of the participants interpret if–then sentences as conditional events. There is, however, a group of about 20% of the participants who inter- pret if–then sentences as conjunctions. We did not observe any other system- atic interpretations, specifically, no material implication or biconditionals.
A stable conditional event interpretation requires the activation of the truth conditions of a conditional event. This can become a routine during working through a sequence of tasks of the same type. The conjunction response does not necessarily imply that the core meaning of the conditional is a conjunction. It may easily be the case that the solution process gets stuck at an intermediate processing step. While building the discourse representa- tion structure, the antecedent is not reprocessed or not assumed to be veri-
fied. This leads to the activation of the truth conditions of a conjunction. Incomplete processing may evoke a sudden shift of the interpretation (Fugard et al.,2011). The binding of the antecedent and the consequent is moderated by the perceived relevance of the antecedent (Skovgaard-Olsen et al.,2016). The remaining 5% of unsystematic interpretations may result from erroneous perceptual scanning or from miscounting.
We see the conditional event interpretation at the core of a process model. This claim is supported by the participants’evaluation of their own responses. Participants with conditional event interpretations were confident that their answers were correct and that they understood the tasks well. The number of conditional event interpretations increased in the course of the experimental sessions. Change-point analyses showed that all changes are from “some” interpretation to a conditional event interpretation, most often from conjunc- tion to conditional event. No one of the 240 participants changed in a differ- ent direction. The Card Task used in the present experiments improved the methodology of the Die Task used in our previous study (Fugard et al.,2011). The number of conditional event interpretations in the present experiments is higher than in our previous one. The improvements in the methodology led to results closer to the present process model.
The logical core of the human understanding of conditionals is the condi- tional event in the sense of de Finetti (Coletti & Scozzafava,2005; de Finetti,
1995,1974). We propose to extend this core meaning by Kamp's and Reyle's (1993) discourse representation theory. The treatment of the comprehension
of conditionals in this theoryfits nicely the suppositional approach of Evans et al. (2003) and Over and Evans (2003). We try to explain the sequential cog- nitive processing of conditionals by a simple discourse representation model. To encode the meaning of a conditional requires at least three steps: (i) repre- senting the antecedent, (ii) extending the representation by the pair (ante- cedent, consequent), and (iii) going back to the antecedent and assuming it to be verified. The conjunction interpretation gets stuck in the second step, takes the pair (antecedent, consequent) as a conjunction and thus neglects to reprocess the antecedent and to see the conjunction on the background of the antecedent. As a consequence in the Card Task, the count of the (object, colour) or (colour, object) cards is not standardised by the count of the ante- cedent cards. Only the cards matching those objects and colours mentioned in the conditional are counted.
We found a weak but reliable correlation between conditional event inter- pretations and working memory, measured by the number of lure-3 responses in the 2-back task. Memory control processes protect against inter- ference and block competing memory material (Oberauer, 2005; Oberauer et al., 2012). These processes organise the various passes in the Kamp and Reyle model and block lures in the n-back task. Working memory is conceived as an efficient attention control system, not as the size of a memory buffer. The experiments reported by Unsworth (2015) investigated the relationship between reasoning tasks and working memory capacity. The reasoning tasks they used, however, were mainly intelligence tests (Raven test, Cattell's cul- ture fair intelligence test), not tasks specifically related to deductive or induc- tive reasoning. Compare also Markovits and Barrouillet (2002), Markovits, Doyon, and Simoneau (2002), and Halford, Andrews, and Wilson (2015).
The conjunction interpretation of a conditional does not loop back to the antecedent (step e in Figure 3). It does not re-standardise the conjunction probability in terms of the probability of the antecedent. The discourse repre- sentation structure involves the same looping back to an already processed entity. Such an “inhibition of return” (IOR) is described in the research on visual attention and refers to the inhibition to attend two times in succession to the same location (Logan,1994).
The game-theoretical semantics suggests the speculation of an inner dia- logue. It suggests a relationship to Johnson-Laird's theory of mental models. The theory proposes a final processing stage in which reasoners test their conclusions by a search for counter-examples. This may well involve a“virtual theater” where different players exchange arguments which attack and defend assumptions or consequences. Especially, the conditional event inter- pretation (Figure 4) requires to hypothetically switch roles and to search for wins or losses.
With respect to the order of objects (“The card shows a car”) and colours (“The card shows red”), we replicated thefinding of our previous experiment
(Fugard et al.,2011). At the beginning of the experiments, responses for the object-colour order are faster than for the colour-object order and the rela- tionship reverses towards the end of the sequence. Similarly, at the begin- ning, object–colour tasks produce slightly more conditional event interpretations than at the end. A plausible explanation is that the recognition of the colour of the objects is easy and fast and the participants learn during the course of the experiment to attend to the colourfirst.
The X-out-of-Y response format requires a warning. It might suggest that conditional probabilities can only be assessed with the help of two probabili- ties, the probability of a conjunction and the probability of the conditioning event. This is not true. Conditional probabilities may be assessed directly. All that is needed is to mark the conditioning event ashypothetically true(see
Mark as suppositionalin the process model under point (e)). This constrains the universe of possibilities. In the Card Task, the X-out-of-Y format functions as a trick to distinguish the conditional event interpretation from a series of other interpretations.
A deficit in the probabilistic approach to reasoning is the poor embedding into theories on cognitive processing (Kleiter, 1987). What Oberauer says about working memory applies to our own work as well:“...theories on work- ing memory in general, have so far remained verbal descriptions of mecha- nisms. This is problematic because it is generally acknowledged that working memory is a complex system, and comprehensive theories of working mem- ory typically assume numerous mechanisms and processes that operate together ...”(Oberauer et al.,2012, 780).
A good theory of the human understanding of connectives in reasoning and problem solving requires the integration of several cognitive models including models on: their formal interpretation, the steps involved in their encoding in discourse processing, their pragmatics, their roles in deontic, causal, couterfactual, and argumentative contexts, the role of semantic mem- ory, of knowledge and beliefs, the representation of uncertainty and vague- ness, the role of working memory, attention, and control, the role of individual differences (including gender), and cognitive development.